The Wrong Comparison

In graduate school, I had the privilege of taking a course in field theory taught by David Gross. That's not a household name, I know, but it's a big name in physics … he was one of the folks involved in the construction of the Standard Model in the early '70s. If you read about quantum chromodynamics (QCD) in, say, Scientific American, you'll learn that although quarks are tightly bound, they appear free at high energies … last year Gross and two others shared the Nobel Prize for figuring that out.

If anybody from school happens to read this, don't get me wrong … there were plenty of other courses that it was a privilege to take. However, I'm not writing about privileges, I'm writing about a particular experience I had in Gross' course.

So, what was the course like? Well, on the one hand, it was very educational; I learned many interesting new things. On the other hand, it gave me a huge inferiority complex. Sure, I often understood the basic facts Gross was trying to convey, but I didn't understand all the relationships between the facts, much less all the little notes and asides he'd throw in. I was really down on myself because I didn't understand it all just like he did.

It wasn't until a few years later, I think, that I realized I'd been making the wrong comparison. I'd been listening to one of the world's top physicists, who had been practicing field theory full time for over twenty years … of course I hadn't understood it all just like he did! In other words, the comparison was valid, but it wasn't useful, except to the extent that it spurred me to learn more.

I still think of that experience once in a while, when I see myself or someone else making the same mistake. I wish I could present you with some nice conclusion about comparisons that are valid but not useful, but I've never really gone beyond identifying the mistake. Here are some attempts at conclusions … but don't take them too seriously, since I just made them all up.

Avoid making comparisons that are valid but not useful.

When making comparisons, be sure to take all factors into account.

The grass is always greener on the other side of the fence.

Be aware of the fact that your mind likes to compare things, to juxtapose them, even when the result isn't useful.

I like that last one a lot, but I ought to point out that it and the one before it are weaker conclusions, in a sense. They don't suggest any course of action, they only provide information. In other words (see Some Memes), they're factual, not strategic. (Whether or not they're true is a whole different matter.)

Now let me back up and fix something I glossed over. I talked about making the same mistake, but what counts as the same depends on how far you want to slide along the scale from specific to general. At one end, there's comparing yourself to David Gross (not a mistake if you're one of his peers, or if you're him); at the other end, there's making a comparison that's valid but not useful. Above, I just jumped all the way to the other end, but in the process I think I lost the essence of the mistake. To see what that essence is, let's look at two other examples that I think truly represent the same mistake.

The first example has to do with people who appear in the news. It's so easy to compare myself to them … stupid, but still easy. Do I have the money of Bill Gates, or even of a successful local businessman? No. Do I have the power of the President, or of a city councilman? No. Do I have a series of gorgeous girlfriends and/or wives, like a movie star? No. It's easy for me to make these comparisons and let them get me down, but they're all completely wrong. The people in the news are almost by definition statistical outliers.

The second example has to do with history (or, in fact, with anything that has a historical setting, fictional or not). History tends to be about kings and countries and great events … think, for example, of any event in Europe over the past thousand or so years. So, when I think of history, I think of kings and the nobility, and then naturally I tend to compare myself to them. And what do I see? I'm not master of a castle; I have to work to support myself; I even have to cook my own meals … life sure is rough here in the 21st century, isn't it?

Of course those comparisons are wrong too, in two ways. First, I'm not taking all factors into account. The kings of Europe may have had many good things, but they also didn't have many of the good things that I do, things like grocery stores, running water, and indoor plumbing. Second, as above, I'm thinking of people who are statistical outliers. It would be hard to compare myself unfavorably to the average peasant.

So, now I can tell you what I think is the essence of the mistake. Not taking all factors into account has nothing to do with it. Comparing apples to oranges is close; comparing apples to unusually large apples is right on target. One could stop there, that's a good generalization, but to me it doesn't seem like the same mistake unless people are involved. What about comparing average people to statistical outliers? Comparing all women to supermodels, say? That's a mistake, yes, but still not quite the same mistake … the person making the comparison should also be at one end of it, the short end. And there you have it.